SIAM Journal on Control and Optimization, Volume 59, Issue 3, Page 2121-2146, January 2021.
In this paper, we study a time-inconsistent consumption-investment problem with random endowments in a possibly incomplete market under general discount functions. We provide a necessary condition and a verification theorem for an open-loop equilibrium consumption-investment pair in terms of a coupled forward-backward stochastic differential equation. Moreover, we prove the uniqueness of the open-loop equilibrium pair by showing that the original time-inconsistent problem is equivalent to an associated time-consistent one.

中文翻译：

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一般贴现函数下不完全市场中的时间不一致消费-投资问题

SIAM Journal on Control and Optimization，第 59 卷，第 3 期，第 2121-2146 页，2021
年1 月。在本文中，我们研究了在一般贴现函数下可能不完整市场中具有随机禀赋的时间不一致消费-投资问题。我们根据耦合的前向-后向随机微分方程为开环均衡消费-投资对提供必要条件和验证定理。此外，我们通过证明原始时间不一致问题等价于相关的时间一致问题来证明开环平衡对的唯一性。